Details

Time bar (total: 9.0s)

sample27.0ms

Algorithm
intervals
Results
14.0ms275×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
28.7b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
10.0ms
(- (* x.im y.re) (* x.re y.im))
25.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series133.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* y.re y.re) (* y.im y.im))
32.0ms
(- (* x.im y.re) (* x.re y.im))
77.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0316555
11343496
25001481

prune342.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.5b
(- (* x.im y.re) (* x.re y.im))
16.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
11.0ms
(/ 1 (* (hypot y.re y.im) 1))
52.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
8.0ms
(- (* x.im y.re) (* x.re y.im))
18.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series346.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1 (* (hypot y.re y.im) 1))
162.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
32.0ms
(- (* x.im y.re) (* x.re y.im))
107.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05551207
123061003
25003995

prune605.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
16.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
18.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
22.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series253.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
37.0ms
(- (* x.im y.re) (* x.re y.im))
106.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify51.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04511408
116591307
250011298

prune727.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
5.7b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
11.3b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
1644×times-frac
785×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
624×sqrt-prod
161×associate-/l*
38×div-inv
20×add-exp-log add-cbrt-cube
15×associate-/r*
10×cbrt-undiv div-exp
6×div-sub add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×frac-2neg clear-num
2×flip3-- flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 805
Calls
4 calls:
59.0ms
(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
25.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
20.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
32.0ms
(- (* x.im y.re) (* x.re y.im))
103.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
181.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

simplify176.0ms

Algorithm
egg-herbie
Counts
817 → 817
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0205917108
1500115590

prune4.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

regimes292.0ms

Accuracy

31.8% (8.7b remaining)

Error of 13.2b against oracle of 4.5b and baseline of 17.3b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03032
13032

end0.0ms

sample580.0ms

Algorithm
intervals
Results
368.0ms8508×body80valid